TY - JOUR
AU - Bazovkin, Pavel
AU - Mosler, Karl
PY - 2012/05/17
Y2 - 2024/10/06
TI - An Exact Algorithm for Weighted-Mean Trimmed Regions in Any Dimension
JF - Journal of Statistical Software
JA - J. Stat. Soft.
VL - 47
IS - 13
SE - Articles
DO - 10.18637/jss.v047.i13
UR - https://www.jstatsoft.org/index.php/jss/article/view/v047i13
SP - 1 - 29
AB - Trimmed regions are a powerful tool of multivariate data analysis. They describe a probability distribution in Euclidean d-space regarding location, dispersion, and shape, and they order multivariate data with respect to their centrality. Dyckerhoff and Mosler (2011) have introduced the class of weighted-mean trimmed regions, which possess attractive properties regarding continuity, subadditivity, and monotonicity. We present an exact algorithm to compute the weighted-mean trimmed regions of a given data cloud in arbitrary dimension d. These trimmed regions are convex polytopes in Rd. To calculate them, the algorithm builds on methods from computational geometry. A characterization of a regionâ€™s facets is used, and information about the adjacency of the facets is extracted from the data. A key problem consists in ordering the facets. It is solved by the introduction of a tree-based order, by which the whole surface can be traversed efficiently with the minimal number of computations. The algorithm has been programmed in C++ and is available as the R package WMTregions.
ER -